Mathematical Model of Mechanical Virion-Cell Interaction During Early Engulfment in HIV

Abstract

AbstractWhile HIV entry into host cells has been extensively studied from a biological and biochemical perspective, the influence of mechanical parameters of virions and cells on engulfment and invagination is not well understood. The present work aimed at developing a mathematical model to quantify effects of mechanical and morphological parameters on engulfment forces and energies of HIV particles. Invagination force and engulfment energy were described as analytical functions of radius and elastic modulus of virion and cell, ligand-receptor energy density, receptor complex density, and engulfment depth for early stage engulfment. The models were employed to study the effects of (a) virion-membrane contact geometry on required invagination force for global cell geometries and ultrastructural cell membrane features, and (b) virion radius and number of gp120 proteins on engulfment energy. The invagination force was equal for cells of various sizes (i.e. macrophages and lymphocytes), but lower when considering ultrastructural membrane. The magnitude of the normalised engulfment energy was higher for a mature than for an immature, larger virion with the same number of 72 gp120 spikes, but it decreased for a mature virion with a reduced number of gp120 spikes. The results suggest that for early stage engulfment (1) localised cell membrane features promote invagination and may play a role in entry ability, and (2) shedding of gp120 proteins during maturation reduces engulfment energy which is expected to reduce entry ability.